Modeling of Sheet Metal Forming Based on Implicit Embedding of the Elasto-Plastic Self-Consistent Formulation in Shell Elements: Application to Cup Drawing of AA6022-T4

This article is concerned with multilevel simulations in sheet metal forming using a physically based polycrystalline homogenization model that takes into account microstructure and the directionality of deformation mechanisms acting at single-crystal level. The polycrystalline-level model is based on the elasto-plastic self-consistent (EPSC) homogenization of single-crystal behavior providing a constitutive response at each material point, within a boundary value problem solved using shell elements at the macro-level. A recently derived consistent tangent stiffness is adapted here to facilitate the coupling between EPSC and the implicit shell elements. The underlining EPSC model integrates a hardening law based on dislocation density, which is calibrated to predict anisotropic hardening, linear and nonlinear unloading, and the Bauschinger effect on the load reversal for AA6022-T4. To illustrate the potential of the coupled multilevel finite element elasto-plastic self-consistent (FE-EPSC) model, a simulation of cup drawing from an AA6022-T4 sheet is performed. Results and details of the approach are described in this article.